Transmuted Inverse Loglogistic Model: Properties and Application in Medical Sciences and Engineering

Abstract

In this article, we introduced a two parameter Transmuted model of Inverse Log-logistic Distribution (TILLD) using the quadratic rank transmutation map technique studied by Shaw and Buckley [1]. We provide a comprehensive description of the statistical properties of the TILLD. Robust measures of skewness and kurtosis of the proposed model have also been derived along with the moment generating function, characteristic function, reliability function and hazard rate function of the said model. The estimation of the model parameters is performed by maximum likelihood method followed by a Monte Carlo simulation procedure. The applicability of this distribution to modeling real life data is illustrated by two real life examples and the results of comparison to base distribution in modeling the data are also exhibited.

Key Words: Transmuted Inverse Log-logistic Distribution (TILLD), Survival Analysis, Robust measures, Monte Carlo Simulation.